%% dirty hack
\begin{Russian}
\def\acknowledgmentsname{Благодарности}
\end{Russian}

\begin{acknowledgments}

% \begin{Lncs}
% \begin{English}
% % \paragraph{Notes and Comments}
% \subsubsection*{Acknowledgments.}
% \end{English}
% \end{Lncs}


% \begin{Russian}
%   Публикация подготовлена при поддержке Программы РУДН «5-100»
%   (получатель A.A., разработка математической модели). Исследование
%   выполнено при финансовой поддержке РФФИ в рамках научного проекта No
%   20-01-00001 (получатель B.B., разработка имитационной
%   модели). Исследование выполнено при финансовой поддержке РФФИ в
%   рамках научного проекта No 20-01-00002 (получатель C.C., проведение
%   численного анализа).
% \end{Russian}
% \begin{English}
%   The publication has been prepared with the support of the ``RUDN
%   University Program 5-100'' (recipient A.A., mathematical model
%   development). The reported study was funded by Russian Foundation
%   for Basic Research (RFBR), project number 20-01-00001 (recipient
%   B.B., simulation model development). The reported study was funded
%   by Russian Foundation for Basic Research (RFBR), project number
%   20-01-00002 (recipient C.C., numerical analysis).
% \end{English}

\begin{Russian}
Публикация выполнена при поддержке Программы стратегического
академического лидерства РУДН.
% и при финансовой поддержке РФФИ в рамках научного проекта
% \textnumero~19-01-00645.
%
% Расчёты проведены на вычислительном кластере «Felix» РУДН и на
% Гетерогенном вычислительном кластере «HybriLIT» Многофункционального
% центра хранения, обработки и анализа данных ОИЯИ.
\end{Russian}
\begin{English}
This paper has been supported by the RUDN University Strategic Academic Leadership Program.
% and funded by Russian Foundation for Basic Research (RFBR) according to the research project
% No~19-01-00645.

% The computations were carried out on the Felix computational cluster
% (RUDN University, Moscow, Russia) and on the HybriLIT
% heterogeneous cluster (Multifunctional center for data storage,
% processing, and analysis at the Joint Institute for Nuclear
% Research, Dubna, Russia).
\end{English}

\end{acknowledgments}

% Acknowledgments
% The theoretical part of the work was done under Russian Science Foundation grant No. 14-11-
% 00485 “High performance methods and technologies of modelling the electrophysical processes
% and devices”. The numerical experiments were performed with support of Russian Foundation
% for Basic Research grants No. 16-31-00301 “Development of efficient parallel algorithms
% for numerical simulation of ultrarelativistic beams of charged particles”, No. 16-01-00209
% “Computer simulation unstable modes of interaction relativistic electron bunches with plasma
% in the CNF facilities”, No. 14-01-00392 “Development of the effective parallel algorithms for
% modeling the processes in the relativistic plasma physics”, and No. 14-07-00241 “Template
% implementation of Particle-In-Cell method for solution of plasma physics problems with hybrid
% supercomputers”.

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